[1]} explains that the Cut-model approach to inference using (REF ) is Bayesian Multiple Imputation (BMI), in essence a two-stage process: at the imputation stage the posterior distribution \(\pi (\varphi \mid Z)\)  of \(\varphi \)  is imputed from the data \(Z\)  as if \(\varphi \)  were missing data; in the analysis stage the posterior distribution \(\pi (\theta |Y,\varphi )\)  of \(\theta \)  is conditioned on the imputed \(\varphi \)  so that uncertainty in \(\varphi \)  is fed through into the distribution of \(\theta \) .
